//Given an integer n, return the least number of perfect square numbers that sum
// to n. 
//
// A perfect square is an integer that is the square of an integer; in other wor
//ds, it is the product of some integer with itself. For example, 1, 4, 9, and 16 
//are perfect squares while 3 and 11 are not. 
//
// 
// Example 1: 
//
// 
//Input: n = 12
//Output: 3
//Explanation: 12 = 4 + 4 + 4.
// 
//
// Example 2: 
//
// 
//Input: n = 13
//Output: 2
//Explanation: 13 = 4 + 9.
// 
//
// 
// Constraints: 
//
// 
// 1 <= n <= 104 
// 
// Related Topics 广度优先搜索 数学 动态规划 
// 👍 1097 👎 0


package leetcode.editor.cn;

//Java：Perfect Squares
class P279PerfectSquares {
    public static void main(String[] args) {
        Solution solution = new P279PerfectSquares().new Solution();
        System.out.println(solution.numSquares(12));
        // TO TEST
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {


        public int numSquares(int n) {
            int[] memo = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                memo[i] = i;
                for (int j = 1; i - j * j >= 0; j++) {
                    memo[i] = Math.min(memo[i], memo[i - j * j] + 1);
                }
            }
            return memo[n];
        }

    }
//leetcode submit region end(Prohibit modification and deletion)

}